Question

Show that the following numbers are irrational.

`7sqrt(5)`

Answer 1

 Let us assume that `1/sqrt2` is rational. Then, there exist positive co primes a and b such that

`7/sqrt5=a/b`

`sqrt5=a/(7b)`

We know that `sqrt5` is an irrational number

Here we see that `sqrt5` is a rational number which is a contradiction

Hence `7sqrt5` is irrational.